How to move an object in to the corresponding mirrored coordinate (BGE)?
Sounds like a job for the modulo operator.  The boundary size is hard coded here, so you can delete that boundary cube. Set the worldSize variable to the size you want the boundary to be:

def update(cont):
    own = cont.owner

    own["pos"] = str([round(v) for v in own.worldPosition])

    worldSize = 10

    own.worldPosition[0] = own.worldPosition[0] % worldSize
    own.worldPosition[1] = own.worldPosition[1] % worldSize


And a screenshot for context: